Here is where it gets tricky. I have tools that I install, and tools that are vendor services, that I want to make it look like a subdirectory of: office.mydomain.com

As far as I know, you cannot point a SaaS tool to a subdomain + subdirectory?

For example, I use codiad, which I install on: office.mydomain.com/code/

Then, I use a SaaS service called Only Office that I can white label. Is it possible for me to point the SaaS (there is an option for this) OnlyOffice to "desk.mydomain.com", then redirect "desk.mydomain.com" to "office.mydomain.com/desk/"? Since I cannot point OnlyOffice directly to "office.mydomain.com/desk/". Would codiad at "office.mydomain.com/code/" still work? Would the SSL I install on "office.mydomain.com" still be effective?